Question

In a group of $10$ people, $70$% take vitamins. If you randomly choose $2$ of them, what is the probability that neither person selected takes vitamins?

• A. $.0677$
• B. $.09$
• C. $.30$
• D. $.47$
• E. $.49$

Answer 1

The correct option is A $.0677$

Total no. of people $=10$

$\Rightarrow 70$% of people take vitamins, i.e, $\frac{70}{100}\times 10=7$ people.

$\Rightarrow 30$% of people doesn't take vitamins, i.e, $\frac{30}{100}\times 10=3$ people.

$\Rightarrow P(2$ person who don't take vitamins $)=\frac{{}^3{C}_2}{{}^{10}{C}_2}=\mathrm{0.0677.}$

Hence, the answer is $\mathrm{0.0677.}$